Abstract
We have proposed and analyzed a mathematical model of a predator–prey system where prey is infected but able to reproduce logistically with predators’ linear functional response. The existence, uniqueness and uniform boundedness of solutions are established in the positive octant. The threshold condition for epidemic and the conditions for persistence of the model system are derived. Several equilibria states and their feasibility conditions are found. The system is analyzed for various interesting dynamical behaviors which include boundedness, persistence, local stability, global stability around each of the equilibria. We have also investigated that the system undergoes a Hopf-bifurcation around the disease free equilibrium point. We have studied the direction and stability of the Hopf-bifurcating periodic oscillation. The analytical findings are verified by numerical simulation.
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